Problem: Simplify the expression. $(3t^{2}-3t)(5t^{4}-6t^{2}-3t)$
Solution: First use the distributive property. $ 3 t^2 (5 t^4) + 3 t^2 (-6 t^2) + 3 t^2 (-3 t) - 3 t (5 t^4) - 3 t (-6 t^2) - 3 t (-3 t) $ Simplify. $ 15t^{6} - 18t^{4} - 9t^{3} - 15t^{5} + 18t^{3} + 9t^{2} $ $15t^{6}-15t^{5}-18t^{4}+9t^{3}+9t^{2}$ Identify like terms. $ { 15t^{6}} {- 18t^{4}} {- 9t^{3}} {- 15t^{5}} {+ 18t^{3}} {+ 9t^{2}} $ Add the coefficients. $ { 15t^{6}} { -15t^{5}} { -18t^{4}} {+ 9t^{3}} {+ 9t^{2}} $